BIOL2007- POPULATION GENETICS TUTORIAL - Single locus selection and drift
Due: Friday 25 January, 4:30pm, in Wolfson House 306 coursework box

Use lecture handouts when necessary. Ring tutor or J. Mallet when all else fails!
1) In a study of the peppered moth in Central Birmingham in 1954, the following genotype frequencies were found:
carbonaria  heterozygotes  typica
CC          Cc         cc         Total
394         102         23          519
(note, frequencies of  heterozygotes were obtained by crossing the CC and Cc  x cc typica, and looking at progeny ratios).

a) Estimate the allele frequencies at the C locus, and then, using the Hardy-Weinberg law, find the expected genotypic frequencies.

b) Use these frequencies to estimate the expected numbers of genotypes (which should not be rounded to whole numbers!),
and test for deviation from Hardy-Weinberg using a chi-square goodness of fit test [Note:  , where O=observed numbers, E=expected numbers]; what is the total chi-square value?

c) Look up the probability of getting results this extreme in the following simplified chi-square table

(Note: for a worked example and problems with degrees of freedom, see the lecture on "Evolution of Genetic Diversity"). Write down this P-value.
______________________________________________________________
Degrees of           Value of P
freedom              0.99  0.9   0.5   0.1   0.05  0.01  0.001
1                    0.00  0.02  0.46  2.71  3.84  6.63  10.83
2                    0.02  0.21  1.39  4.61  5.99  9.21  13.82
d) Is there evidence for deviation from Hardy-Weinberg? Write down three possible causes for a deviation (whether there is or isn't).

e) How many C, and how many c alleles were present in the 1954 sample?  How many
C+c alleles in total?

2)  In 1955 the population was resampled and the following data were obtained:

alleles
Year         C          c      Total alleles

1954       890        148         1038
1955       778        110          888

Totals    1668        258         1926

a) Perform a chi-square 2x2 test of homogeneity for allele frequency, to see whether there is any evidence for allele frequency change. Explanation: The expected values are given by assuming that the gene frequencies have not changed between years.  For example, the expected number of C alleles in 1954 is given by a combination of the marginal totals: 1038x1668/1926 =
898.9533. The degrees of freedom for homogeneity tests are given by the formula (r-1)(c-1) where r and c are the numbers of rows and of columns, here (2-1)(2-1) = 1 degree of freedom. Obtain chi-square value as in formula above (Note: you may use Yates' correction if you want, but I will not take marks off for not doing so. Opinions differ as to whether Yates' correction is sensible).

b) What is the chi-square value? (It should be a sum of four numbers).

c) Look up the value of chi-square on the above table.  What is the value of P?

d) What were the allele frequencies? Has there been a significant change in allele frequency?

e) What has the change in gene frequency, , been?

f) Given that there is only one generation per year in this species, what is the selection pressure, s?  Use the formula forgiven in the lecture on single-gene selection. [HINT: if s seems unreasonable, and you have checked your arithmetic, don't worry].

3) There has been a controversy about Bernard Kettlewell's mark-release-recapture experiments. The main controversy is over whether there is evidence for selection due to predation of moths on polluted and unpolluted backgrounds, or whether there is some other cause. Here are four brief book reviews on the controversy (you will need your UCL computer ID and password to download these files; if you don't have one, ask a friend to do it for you, or go directly to the journals):

Anti visual predation: Coyne,JA (1998): Not black and white.  Review of "Melanism: Evolution in Action" by Michael E.N. Majerus. Nature 396, 35-36, and Coyne,JA (2002): Evolution under pressure.  Review of Judith Hooper: "Of Moths and Men: Intrigue, Tragedy and the Peppered Moth. Nature 418, 19-20.
Pro visual predation: Grant,BS (2002): Sour grapes of Wrath. Review of "Of Moths and Men" by Judith Hooper. Science 297, 940-941.
Neutral:  Shapiro,AM (2002): Paint it black.  Review of "Of Moths and Men" by Judith Hooper. Evolution 56, 1885-1886.
News article: Proffitt,F (2004): In defense of Darwin and a former icon of evolution. Science 304, 1892-1895.

a) Based on these brief reviews, what are your thoughts on this controversy (write not more than a paragraph or so)?

b) Do you feel any further experiments are needed.  If so, what?

c) On the basis of this evidence, vote for or against the idea that visual bird predation is a cause of the evolution of melanism in the peppered moth, and its decline since the Clean Air Acts (part (c) will not carry any marks; it is just to assess public opinion!).

4) a) Inbreeding causes a deficit of heterozygotes in the population (see "Inbreeding and Neutral Evolution lecture"). Supposing the numbers of genotypes in an inbred population are: AA 432, Aa 702, aa 1281.  What is the value for F? HINT:Observed heterozygote frequency = 2pq(1-F). Rearrange to solve for F.

I have a son Kevin, who marrys Cath, and has a daughter, Bertha. However, Cath's dad, Fred, is in fact her mother's first cousin and also my own first cousin (see diagram).

b) What is Bertha's inbreeding coefficient, F i.e. the probability that she has an allele at any locus that is identical by descent through my grandparents? Hint: add up the probabilities for any paths that go through both of Bertha's parents (Kev AND Cath). HINT: You should get only four paths.

c) Is it a bad thing to marry so incestuously?